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My normal trick is to use find with the -ls option and sort the output.

find /var -type f -ls | sort -k7n,7n | tail -5

will give you the top five files including their paths by size in /var

You might want to tweak in terms of following (or not following) symbolic links etc - but it is pretty quick. As it uses sort it will use some space while running, but unless you have a VERY big file system that shouldn't be a real problem. Best run as a user having read access over the whole filing system (or you can throw STDERR to /dev/null)